The broad objective of this proposal is to develop new sequential statistical methods for the design and analysis of clinical trials that complement current group sequential methods. Clinical trials demand interim analyses and monitoring for ethical, economical and scientific reasons. The key statistical issue is that repeated interim analyses of accumulating data may seriously invalidate the use of a conventional fixed sample test in comparing the treatments at the end of the trial by inflating the type I error. Therefore clinical trials should utilize a (group) sequential procedures that allow early stopping. Then the issue is, What do we lose in terms of statistical information (in comparison with the fixed sample test) if we stopped the trial early? In stead of using stochastic curtailment that calculates a conditional power, we propose to use a more direct measure that computes the chance that the sequential test and the fixed sample test do not agree. Most importantly, we propose a formal (group) sequential boundary that allows early stopping and retains the validity of a fixed sample design in the following sense: (1) the entire power functions of the fixed sample test and the sequential design are virtually the same; (2) the discordant probability that the sequential test leads to a conclusion opposite to that of the fixed sample test is negligible; (3) the maximum sample size is no greater than the size of the corresponding fixed sample size test; and the expected sample sizes are substantially smaller than the size of the fixed sample test. Therefore, such a sequential plan provides stronger objective evidence to decision makers when early stopping is necessary than do the current group sequential and stochastic conditional probability ratio test and confidence intervals after sequential stopping for trials with normally distributed responses and dichotomous outcomes; (2) to extend the use of discordant probability to clinical trials monitoring; (3) to develop methods for clinical trials with repeated measures data or time-to-event outcomes; (4) to extend the results to multiple repeated measures outcomes, and/or time-to-event outcomes; (5) to extend the fast algorithm for calculating operating characteristics to different trial designs and make the algorithm applicable to current group sequential boundaries as well and compare them; (6) to apply the proposed methods to four NIH sponsored multicenter trials and a cancer trial.